I came across this article from over a year ago which appeared in the N.Y. Times about how we are not teaching students to solve math problems the right way.
In it, the author features a quote from an email she received from Tracy Zager, an author of math ed books:

“I really feel I have no way to have an impact on this teacher’s blind spot since it is shared by all math teachers and so many other teachers: If you don’t understand, it’s your fault. It was never a sensible idea to try to have students memorize first and understand later; this approach to mathematics instruction is structurally flawed. I really feel for these parents and this kid, but the frustration they face is inevitable. If we teach kids math without understanding, we build on a house of cards.”